Broadband wireless systems are currently in a rapid evolutionary phase in terms of development of various technologies, development of various applications, deployment of various services and generation of many important standards in the field. The increasing demand on various services justifies the need for the transmission of data on various communication channels at the highest possible data rates. The multipath and fading characteristics of the wireless channels result in various distortions, the most important of those being the intersymbol interference (ISI) especially at relatively high data rates. Adaptive equalizers are employed to mitigate the ISI introduced by the time varying dispersive channels and possibly arising from other sources. In one class of adaptive equalizers, a training sequence known to the receiver is transmitted that is used by adaptive equalizer for adjusting the equalizer parameter vector to a value that results in a relatively small residual ISI. After the training sequence, the data is transmitted during which period the equalizer continues to adapt to slow channel variations using decision directed method.
Among the various algorithms to adapt the equalizer parameter vector are the recursive least squares (RLS) algorithm, exponentially weighted Kalman filter, LMS algorithm, and the quantized state (QS) algorithm, the last one taught by Kumar et. al. in, “Adaptive Equalization Via Fast Quantized-State Methods”, IEEE Transactions on Communications, Vol. COM-29, No. 10, October 1981. Kumar at. al. teach orthogonalization process to arrive at fast and computationally efficient identification algorithms in,” State Inverse and Decorrelated State Stochastic Approximation”, Automatica, Vol. 16, May 1980. The training approach, however, is not desirable in many communication applications such as those involving video conference type of applications that will require a training sequence every time a different speaker talks. Moreover, the need for training sequence results in a significant reduction in capacity as for example, in GSM standard, a very significant part of each frame is used for the equalizer training sequence. Also, if during the decision-directed mode the equalizer deviates significantly due to burst of noise or interference, all the subsequent data will be erroneously received by the receiver until the loss of equalization is detected and the training sequence is retransmitted and so on.
There are many other applications where the equalizers are applied as in antenna beam forming, adaptive antenna focusing of the antenna, radio astronomy, navigation, etc. For example, Kumar et. al. teach in Method and Apparatus for Reducing Multipath Signal Error Using Deconvolution, U.S. Pat. No. 5,918,161, June 1999, an equalizer approach for a very different problem of precise elimination of the multipath error in the range measurement in GPS receiver. In all of various applications of equalizers and due to various considerations such as the logistics and efficiency of systems, it has been of great interest to have the equalizer adapt without the need for a training sequence. Such equalizers are the termed the blind mode equalizers.
Among some of the approaches to blind mode equalization is the Sato's algorithm that is similar to the LMS algorithm except that it does not have any training period. Kumar in, “Convergence of A Decision-Directed Adaptive Equalizer,” Proceedings of the 22nd IEEE Conference on Decision and Control, 1983, Vol. 22, teaches a technique wherein an intentional noise with relatively high variance is injected into the decision-directed adaptive algorithm with the noise variance reduced as the convergence progressed and shows that the domain of convergence of the blind mode equalizer was considerably increased with the increase in the noise variance at the start of the algorithm. The technique taught by Kumar is analogous to the annealing in the steel process industry and in fact the term simulated annealing was coined after the introduction by Kumar. Lambert et. al., teach the estimation of the channel impulse response from the detected data in, “Forward/Inverse Blind Equalization,” 1995 Conference Record of the 28th Asilomar Conference on Signals, Systems and Computers, Vol. 2, 1995.
Another blind mode equalization method applicable to the case where the modulated data symbols have a constant envelope and known as Goddard or constant modulus algorithm (CMA) is based on minimization of the magnitude square of the estimate of the estimate of the data symbol and a constant that may be selected to be 1. An example of references for the CMA is W. Chung, et. al., “The local minima of fractionally-spaced CMA blind equalizer cost function in the presence of channel noise,” Proc. IEEE International Conference on Acoustics, Speech, and Signal Processing, pp. 3345-8, 12-15 May, 1998.
Some of the prior blind mode equalizers have relatively long convergence period and are not universally applicable in terms of the channels to be equalized and in some cases methods such as the one based on polyspectra analysis are computationally very expensive. The CMA method is limited to only constant envelope modulation schemes such as M-phase shift keying (MPSK) and thus are not applicable to modulation schemes such as M-quadrature amplitude modulation (MQAM) and M-amplitude shift keying (MASK) modulation that are extensively used in wireless communication systems due to their desirable characteristics. Tsuie et. al. in, Selective Slicing Equalizer, Pub. No. US 2008/0260017 A1, Oct. 23, 2008, taught a selective slicing equalizer wherein in a decision feedback equalizer configuration, the input to the feedback path may be selected either from the combiner output or the output of the slicer depending upon the combiner output. Kumar in, Systems and Methods for Adaptive Blind Mode Equalization, U.S. patent application Ser. No. 13/434,498, Mar. 29, 2012, teaches blind mode equalizer with hierarchical architecture.
The prior blind mode equalization techniques are for the case of a single channel that may be the result of combining the signals received over multiple diversity channels before equalization. Such an approach does not take advantage of the differences that may exist among the diversity channels. Some of the algorithms have relatively slow convergence rate and may be limited in terms of their applicability to various modulation formats. It is desirable to have blind mode adaptive equalizers that are efficient for the case of the signal received over dispersive diversity channels, possess robustness and some level of inherent redundancy to avoid convergence to any local minima, have wide applicability without, for example, restriction of constant modulus signals, are relatively fast in convergence, are computationally efficient, have modular configuration to provide a tradeoff between complexity and performance. The equalizers of this invention possess these and various other benefits.